Let be a function which satisfy the equation for all such that

MATHEMATICS · Subjective · IB Diploma Programme · Mathematics: Analysis and Approaches · Functions · Functions

Problem

Let

f(x)

be a function which satisfy the equation

f(xy) = f(x) + f(y)

for all

x > 0, y > 0

such that

f'(1) = 2

. Find the area of the region bounded by the curves

y = f(x), y = |x^3 - 6x^2 + 11x - 6|

and

x = 0